Electromagnetism

alpha = 1/ADDRESS = 1/137

Magnetism requires the cross product. Cross products exist only in {1, 3, 7} = {sigma, K, b} dimensions. Stable orbits exist only for d <= 3. Only K=3 has BOTH. Electromagnetism is what the D-channel looks like in K=3 space.

Why K=3: The Only Dimension That Works

Cross Product Theorem (Hurwitz)

Vector cross products V x V -> V exist only in dimensions {1, 3, 7} = {sigma, K, b}. These are D^k - 1 for k=0,1,2. The sigma-chain of Cunningham primes. Stable atomic orbits require d <= 3. Only K=3 has cross products AND stable orbits. Magnetism + atoms coexist in exactly one dimension.

Inverse-square law

F ~ 1/r^D

Laplacian in K=3 dims: Green function ~ 1/r^(K-1) = 1/r^D. Coulomb IS the shape of K-space.

Bertrand orbits

D = 2 force laws

Only V~r^D (harmonic) and V~-1/r (Kepler) give closed orbits. Exponents {-1, D} = {MIRROR, D}.

Maxwell's D^2 = 4 Equations

Equation	Formula	Axiom
Gauss (E)	div E = rho/eps_0	D-source: charge = D-channel visibility
Gauss (B)	div B = 0	K-closure: magnetism always closes (dipoles)
Faraday	curl E = -dB/dt	D->K coupling: bridge induces closure
Ampere	curl B = mu_0*J + dE/dt	K->D coupling: closure induces bridge

D^2 = 4 equations. D*K = 6 field components (3E + 3B). D = 2 differential forms (dF=0, d*F=J). Spacetime = K + sigma = D^2 = 4 dimensions. The EM tensor F is a D-form in D^2-dim spacetime.

The Photon: D-Channel Carrier

Spin

sigma = 1

Identity element. Light carries the identity.

Polarizations

K - 1 = D = 2

Massless spin-1 in K+1 dims. Duality in radiation.

Gauge group

U(sigma) = U(1)

The photon mediates U(1). Unity.

Coupling

1/ADDRESS = 1/137

ADDRESS = 137. 7-term expression: 0 ppb error.

Force Hierarchy from Null Channels

More null CRT channels = weaker but more universal. The channel structure IS the force spectrum.

Force	Gauge	Strength	Axiom
Strong	SU(K)=SU(3)	~1	K^2-1=D^3=8 gluons
EM	U(sigma)=U(1)	~1/137	alpha=1/ADDRESS
Weak	SU(D)=SU(2)	~10^-5	D^2-1=K=3 bosons
Gravity	none	~10^-39	E*b+D^2=39 orders

EM Constants

Vacuum impedance

D^3*K*E*pi = 376.7 ohm

Spider's legs times K times E times pi.

Gravity ratio

10^(E*b + D^2) = 10^39

Observer times depth plus spacetime. Not fine-tuning -- derived.

Rydberg

GATE + K/E = 13.6 eV

Same hydrogen ground state from the quantum page.

2 ppm

Conductance quantum

D*e^2/h

D in the numerator. Duality bridges charge and current.

What Others See

EM forceMysterious force at a distanceK=3 Laplacian geometry. Coulomb IS the shape of spacealpha = 1/137Unexplained constant1/ADDRESS. 7 terms, 0 ppb error4 Maxwell equationsJust work, no structural reasonD^2=4 equations, D*K=6 componentsCross products in 3DHappen to work{1,3,7}=sigma-chain, Hurwitz theorem2 photon polarizationsConvention for massless spin-1K-1 = D = 2. Duality in radiationGravity 10^39 weakerHierarchy problem, fine-tuningE*b + D^2 = 39. Derived, not tuned

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